There have been many conflicting interpretations and definitions of Marxism. A year before his death, Marx remarked to his son-in-law, Paul Lafargue, "What is certain is that I am no Marxist!"

It is by no means certain that Marx's work does form an organic whole. Although his basic analytic method was consistent, he developed new conclusions as he applied it to new material. Moreover, he died before finishing Capital.

Karl Marx

Since Marx's death in 1883, various revolutionaries around the world have appealed to Marxism as the intellectual basis for their politics and policies, which can be dramatically different and conflicting. Marxism was the ideology that inspired the creation of the Soviet Union, and post World War 2 political Communism. Although there are still many Marxist revolutionary movements and political parties around the world, relatively few countries have Marxist governments in power. Cuba, North Korea, and the People's Republic of China have governments in power which describe themselves as Marxist.

Hegel proposed a form of idealism in which ideas gradually developed in history. Marx retained Hegel's emphasis on history, but stood Hegel on his head in proposing that material circumstances shape ideas, instead of the other way around.
Marx summarizes his material theory of history, otherwise known as historical materialism, in A Contribution to the Critique of Political Economy:

In the social production of their existence, men inevitably enter into definite relations, which are independent of their will, namely relations of production appropriate to a given stage in the development of their material forces of production. The totality of these relations of production constitutes the economic structure of society, the real foundation, on which arises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life conditions the general process of social, political and intellectual life. It is not the consciousness of men that determines their existence, but their social existence that determines their consciousness.

Marx emphasized that the development of material life will come into conflict with the superstructure. These contradictions, he thought, were the driving force of history. Marx illustrated his ideas most prominently by the development of capitalism from feudalism and by the prediction of the development of socialism from capitalism.

Capital (Das Kapital) is written over three volumes, of which only the first was complete at the time of Marx's death. The first volume, and especially the first chapter of that volume, contains the core of the analysis. Hegel's legacy is especially overpowering here, and the work is seldom read with the thoroughness Marx urges in his introduction. The method of presentation proceeds from the most abstract concepts, incorporating one new layer of determination at a time and tracing the effects of each such layer, in an effort to arrive eventually at a total account of the concrete relationships of everyday capitalist society. This investigation is commonly taken to commit Marx to a species of labor theory of value.

Marx critiqued Smith and Ricardo for not realizing that their economic concepts reflected specifically capitalist institutions, not innate natural properties of human society, and could not be applied unchanged to all societies. Marx's theory of business cycles; of economic growth and development, especially in two sector models; and of the declining rate of profit, or crisis theory, are other important elements of Marxist economics.

The Austrian School were the first liberal economists to systematically challenge the Marxist school. This was partly a reaction to the Methodenstreit when they attacked the Hegelian doctrines of the Historical School. Though many Marxist authors have attempted to portray the Austrian school as a bourgeois reaction to Marx, such an interpretation is untenable: Carl Menger wrote his Principles of Economics at almost the same time as Marx was completing Das Kapital. The Austrian economists were, however, the first to clash directly with Marxism, since both dealt with such subjects as money, capital, business cycles, and economic processes. Eugen von Boehm-Bawerk wrote extensive critiques of Marx in the 1880s and 1890s, and several prominent Marxists--including Rudolf Hilferding--attended his seminar in 1905-06.

the working class or proletariat: Marx defined this class as "those individuals who sell their labor and do not own the means of production" whom he believed were responsible for creating the wealth of a society (buildings, bridges and furniture, for example, are physically built by members of this class). The proletariat may be further subdivided into the ordinary proletariat and the lumpenproletariat, those who are extremely poor and cannot find legal work on a regular basis. These may be prostitutes, beggars, or homeless people.

the bourgeoisie : those who "own the means of production" and employ the proletariat. The bourgeoisie may be further subdivided into the very wealthy bourgeoisie and the petty bourgeoisie: those who employ labor, but also work themselves. These may be small proprietors, land-holding peasants, or trade workers.

Marx developed these ideas to support his advocacy of socialism and communism: "The philosophers have only interpreted the world differently; the point is, to change it." Communism would be a social form wherein this system would have been ended and the working classes would be the sole beneficiary of the "fruits of their labour".

Socialists often (or, in varying degrees) do not recognize an individual right to private property. At any rate, socialist philosophers have argued that there is not a specific right to private property, though it might be in the best interest of society in general for certain individuals to have exclusive control over certain goods, so long as this control does not lead to the class divisions and exploitation of the working class they seek to eliminate. Critics have said that "socialism is a system in which everyone is equally poor", arguing that because individuals are not rewarded more on the basis of supply and demand, there is less incentive for individual achievement, improving technology, and other factors that result in a higher standard of living.

Some of these ideas were shared by anarchists, though they differed in their beliefs on how to bring about an end to the class society. Socialist thinkers suggested that the working class should take over the existing capitalist state, turning it into a workers revolutionary state, which would put in place the democratic structures necessary, and then "wither away". On the anarchist side people such as Mikhail Bakunin and Peter Kropotkin argued that the state per se was the problem, and that destroying it should be the aim of any revolutionary activity.

Many governments, political parties, social movements, and academic theorists have claimed to be founded on Marxist principles. Social democratic movements in 20th century Europe, the Soviet Union and other Eastern bloc countries, Mao and other revolutionaries in agrarian developing countries are particularly important examples. These struggles have added new ideas to Marx and otherwise transmuted Marxism so much that it is difficult to specify its core.

It is usual to speak of Marxian theory when referring to political study that draws of the work of Marx for the analysis and understanding of existing (usually capitalist) economies, but rejects the more speculative predictions that Marx and many of his followers made about post-capitalist societies.

The 1917 October Revolution, led by Vladimir Lenin and Leon Trotsky was the first large scale attempt to put Marxist ideas about a workers' state into practice. However, counterrevolution, civil war, foreign interventions and the failure of a socialist revolution in Germany and in the other western countries gave Joseph Stalin the opportunity to take over power when Lenin died. As predicted by Lenin, Trotsky and others already in the 1920s, Stalin's "socialism in one country" was unable to maintain itself, and according to some Marxist critics, the USSR ceased to show the characteristics of a socialist state long before its formal dissolution.

Following World War II, Marxist ideology, often with Soviet military backing, spawned a rise in revolutionary Communist parties all over the world. Some of these parties were eventually able to gain power, and establish their own version of a Marxist state. Such nations included the People's Republic of China, Vietnam, Romania, East Germany, Albania, Poland, Cambodia, Ethiopia, South Yemen, and others. In some cases, these nations did not get along. The most notable example was the rift that occurred between the Soviet Union and China, whose leaders disagreed on certain elements of Marxism, and how it should be implemented into society.

Many of these self-proclaimed Marxist nations (often styled People's Republics) eventually became authoritarian states, with stagnating economies. This caused some debate about whether or not these nations were in fact led by "true Marxists." Critics of Marxism speculated that perhaps Marxist ideology itself was to blame for the nations' various problems. Followers of the currents within Marxism which opposed Stalin, principally cohered around Leon Trotsky, tended to locate the failure at the level of the failure of world revolution: for communism to have succeeded, they argue, it needed to encompass all the international trading relationships that capitalism had previously developed.

In 1991 the Soviet Union collapsed and the new Russian state ceased to identify itself with Marxism. Other nations around the world followed. Since then, radical Marxism or Communism has generally ceased to be a prominent political force in global politics, and has largely been replaced by more moderate versions of democratic socialism.